Unless you really need 300mm I am not sure why you would get rid of your 70-200F4. The 70-300L is a great lens but the 70-200 is just as good if not better. For that matter, if you need 300, I am not sure why you would consider the 135 instead of it as well.

The 135 is one of the sharpest lenses Canon makes. The 70-300 gives you a lot more flexibility. Do you need those extra focal lengths or not. If you do but go with the 135, you will end up buying another zoom at some point as well.

If I had the 70-200 and needed an ultra sharp F2 lens, I would keep it and buy the 135.

I don't know $1,000 for a lens that is a one trick pony seems kind of crazy. I'd just suggest that he gets the Sigma 70-200 2.8 OS and a 2X TC for when he needs 300-400mm.